Technically, yes, there is a "radio" in your TI-84. The Z-80 is clocked by a crystal oscillator, which runs at a few MHz. Some of that energy will escape in the form of electromagnetic radiation. Sensitive instruments (including an ordinary AM radio) can pick up this radiation from distances ranging from a few inches to several yards. This is true of essentially all modern electronics, although the frequencies have obviously gone higher and higher over time.
If it were true that the RF energy levels emitted by FCC Part 15-covered consumer electronics could interfere with aircraft systems, it would be utterly unthinkable to permit them on board in the first place, whether "powered off" or not. The TSA would be confiscating Game Boys, not bottles of water. Since that isn't happening, it's difficult to avoid the conclusion that the prohibition is just one more exercise in bureaucratic security theatre.